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Tangent Circles

The locus of ...

Question

The locus of the centre of a circle which touches externally the circle, $x^{2} + y^{2} - 6 x - 6 y + 14 = 0$ and also touches the y-axis is given by the equation:

A

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B

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C

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D

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Solution

The correct option is D

Let $(x_{1}, y_{1})$ be a point in the locus

$(x - x_{1})^{2} + (y - y_{1})^{2} = (x - 3)^{2} + (y - 3)^{2} = 2^{2}$

$A p p l y r_{1} + r_{2} = c_{1} c_{2}$

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